No abstract

We show the existence of Yang-Mills-Higgs (YMH) fields over a Riemann surface with boundary where a free boundary condition is imposed on the section and a Neumann boundary condition on the connection. In technical terms, we study the convergence and blowup behavior of a sequence of Sacks-Uhlenbeck type α-YMH fields as α → 1. For α > 1, each α-YMH field is shown to be smooth up to the boundary under some gauge transformation. This is achieved by showing a regularity theorem for more general coupled systems, which extends the classical results of Ladyzhenskaya-Ural'ceva and Morrey.

ABSTRACT. We prove the energy identity and the no neck property for a sequence of smooth extrinsic polyharmonic maps with bounded total energy.